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Ukrainian Mathematical Journal

, Volume 55, Issue 5, pp 801–811 | Cite as

Best “Continuous” n-Term Approximations in the Spaces \(S_\phi ^p \)

  • A. I. Stepanets
  • V. I. Rukasov
Article

Abstract

We find exact values of upper bounds for the best approximations of q-ellipsoids by polynomials of degree n in the spaces \(S_\phi ^p \) in the case where the approximating polynomials are constructed on the basis of n-dimensional subsystems chosen successively from a given orthonormal system ϕ.

Keywords

Orthonormal System 
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REFERENCES

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    A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 2, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2002).Google Scholar
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    A. I. Stepanets, “Approximation characteristics of the spaces S ?p,” [in Russian], Preprint No. 2, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2001).Google Scholar
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    A.I. Stepanets, “Approximation characteristics of the spaces S?p in different metrics,” Ukr. Mat. Zh., 53 No. 8 1121–1146 (2001).Google Scholar
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    A.I. Stepanets, Approxiamtion Characteristics of the Spaces S p [in Russian], Preprint No. 2, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2001).Google Scholar
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    A. I. Stepanets and A. S. Serdyuk, “Direct and inverse theorems on the approximation of functions in the space S p,” Ukr. Mat. Zh., 54, No. 1, 106–124 (2002).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • A. I. Stepanets
  • V. I. Rukasov

There are no affiliations available

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